The twelve months January, February, March, .........., November and December (in that order) of a year are respectively assigned the values 0,1,2,.....,10 and 11.
A given month corresponding to a specific year is defined as succinct when the remainder obtained by dividing a given year by 12 precisely corresponds to the value assigned to a month containing five Sundays. For example, 1990 when divided by 12 yields a remainder of 10; but November, 1990 did not contain five Sundays. Consequently November, 1990 was not a succinct month.
Considering all the succinct months occurring between 1945 A.D. and 2176 A.D. inclusively in accordance with the Gregorian calendar system, when does the 50th succinct month occur?
Determine the maximum number of years between two consecutive succinct months in the stated period.